Here is what I have observed on my Samsung Galaxy SIII running Android Jelly Bean 4.3:

Solid Red LED Light - The device is powered off or screen has gone blank and device is charging.

Solid Green LED Light - The device is powered off or screen has gone blank and device charging is complete.

Solid Blue LED Light - The device has been powered on, has displayed the model name (on my phone "GT-i9300") as part of the first phase of the bootup process, and is now in the second phase of the bootup process which begins with the screen displaying the "Samsung" animated logo and finishes with the Lock screen showing up (or the Home screen if the Lock screen has been disabled). The blue LED light also shows up when the device is powering down.

Blinking Red LED Light - This can happen when the device is off or turned on but the screen has gone blank, and the battery was very low (this displays regardless of whether the phone is being charged or not).

Blinking Blue LED Light - The device is on, the screen has gone blank, and you have received one or more notifications.

Blinking Green LED Light - This is possible in theory, but I've never seen it. Applications could cause this behavior to happen. Probably requires the phone to be rooted though, I'm not really sure.

As I was able to verify when entering the search term LED in the Google Play Store, some devices with more capable LEDs are also able to display wider ranges of LED colors.

EDIT:

Here is a screenshot of the Settings -> My device -> LED indicator screen, which displays most of this information while also allowing the user to customize it: